Intel® oneAPI Math Kernel Library
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## Fastest method to sum matrix

Beginner
579 Views
Hello,

I want to take the sum of a product of two symmetric matrices, meaning that if A and B are symmetric matrices than I want to compute
c=sum(A*B)
where c is a scalar and the multiplication is done element wise. Is there some way to do this by using an MKL routine or is the fastest method using the default compiler commands?

1 Solution
Honored Contributor III
579 Views
It seems to me that you really do not want a matrix product, but the scalar product of two vectors (i.e., 1-D arrays) that happen to be mis-arranged as square matrices. Look up the reshape function in your Fortran manual, so that you can cast the operation that is desired by you into an equivalent scalar product evaluation.
4 Replies
Honored Contributor III
580 Views
It seems to me that you really do not want a matrix product, but the scalar product of two vectors (i.e., 1-D arrays) that happen to be mis-arranged as square matrices. Look up the reshape function in your Fortran manual, so that you can cast the operation that is desired by you into an equivalent scalar product evaluation.
Beginner
579 Views
That seems like a good idea, do you think it will be worth my time to work with 1D arrays (which will make the code very unreadable) or just do a reshape every time (this product will occur a lot of times using matrices which are typically (1024,1024) big, so basically I'm asking if the reshape command is very time consuming)

Beginner
579 Views
Is there some routine other than reshape that converts a symmetrical matrix into a packed scheme?
Honored Contributor III
579 Views
Fortran has always allowed argument association between multidimensional arrays and one-dimensional arrays, as in the example below. Note that this will not work if you use subroutine arguments of assumed shape.

```[fortran]program treshape
integer A(3,3)
data  A/11,12,13,21,22,23,31,32,33/
call sub(A,3*3)
end program treshape

subroutine sub(A,n)
integer A(n)
write(*,10)(i,A(i),i=1,n)
10 format(I4,2x,I4)
return
end subroutine sub
[/fortran]```
Converting a dense matrix to packed or banded matrices is straightforward. Read the section on matrix storage schemes in the MKL manual.